Known as the sequel to the SNES title Super Mario World 2: Yoshi's Island, Yoshi's Story continues within the platform genre, presenting gameplay similar to its predecessor. However, Yoshi's Story turns in a more puzzle-oriented direction, with the aspect of challenge being foremost tied to the achievement of a high score by strategic means. Taking place within a pop-up storybook, the game features vivid pre-rendered 3D graphics, illustrating worlds that are crafted from different materials, such as cardboard, fabrics, plastic, and wood.

The player may choose between two different game modes from the game's main menu: Story Mode and Trial Mode. Upon entering either mode, the player will be able to select a course, find out which fruit will be the Lucky Fruit, and choose a Yoshi of desired color to play as. However, Trial Mode will be void of courses to play at the start of the game, as these will have to be unlocked by completing them in Story Mode.

On each course, the goal is to fill the Fruit Frame by eating 30 pieces of fruit. These may be found in abundance throughout every course, lying around, floating in bubbles, and even carried by some enemies. The player can choose to eat everything they come across on their path. However, this approach may result in significant portions of the game being missed out, as the true depth of the gameplay lies in exploring every part of the courses. This is further supported by the puzzle element of the game, which encourages the player to apply strategy to achieve a high score. For instance, the player will gain more points from eating one kind of a fruit in a row, and even more so if the fruit is a Favourite Fruit or a Lucky Fruit (see Scoring points). In addition, valuable secrets are hidden throughout every course, that will contribute to summit the total score.

In order to manage their way about the courses, the Yoshis can walk, run, jump, swim, crouch, push boxes, stomp enemies, eat fruit, collect items with their tongue, lay eggs by swallowing edible enemies, throw eggs, pound the ground, sniff, and perform flutter jumps. If Yoshi runs into an enemy or a spiky obstacle along his path, petals are lost from the Smile Meter. The flower shaped meter has a total of eight petals, and indicates Yoshi's health, or mood. If petals are lost, they can easily be restored by swallowing enemies or eating fruit, keeping the player in a comfortable state of platforming.

If Yoshi eats six pieces of the same fruit in a row, a Heart Fruit will come parachuting across the screen. By eating this special item, Yoshi will become Super Happy for a limited time, giving him special powers, including invincibility, infinite eggs, longer tongue, and improved flutter jumps. In addition, if Yoshi performs a ground pound when Super Happy, he can smash all bubbles visible on the screen, while Shy Guys will turn into Lucky Fruit, and peppers will turn into coins. In contrast, should the Smile Meter be reduced to a frown, it will only take one hit before Yoshi collapses. If this happens, the Yoshi is captured by Toadies and brought to Baby Bowser's castle. However, if a Yoshi has been kidnapped, they can still be retrieved if the player succeeds at finding a white Shy Guy and completing the course with him. Notably, though, this character is only available in Story Mode, and can only be found if a Yoshi has been lost. The game will end if all the remaining Yoshis have been captured.

In addition to the six Yoshis that are available at the start of the game, the island is also the home of two additional Yoshis: black and white. In order to unlock them, the player must succeed at finding their eggs and carry them through the course. If the black or white egg is successfully rescued, the respective Yoshi will become available on the Yoshi select screen. However, the black and white Yoshis are exclusive to Story Mode, and can't be found or used in Trial Mode. Unlike the other Yoshis, the black and white Yoshis have certain superior abilities. For starters, they consider all fruit their Favourite Fruit, which in turn will be in favour to the player's score. In addition, the black and white Yoshis like peppers, and may swallow enemies that the other Yoshis would consider bitter, including black Shy Guys. The black and white Yoshis also have more powerful eggs, that will set off a huge blast if the Yoshi is happy, and more powerful ground-pounds that shake the course a lot. If either black or white Yoshi is lost, they can only be retained by rescuing their egg again.